Equation general definition

The units of concentration most frequently encountered in analytical chemistry are molarity, weight percent, volume percent, weight-to-volume percent, parts per million, and parts per billion. By recognizing the general definition of concentration given in equation 2.1, it is easy to convert between concentration units. 

Equation (2.39) is the weight average molecular weight as defined in Sec. 1.8. It is important to note that this result. My = M y, applies only in the case of nonentangled chains where 17 is directly proportional to M. A more general definition of My for the case where 17 a is... 

We recognize that 0id majority merely a special case of the generalized threshold rule defined in equation 5.121. In particulm-, majority may be defined using that more general definition by setting... 

Equation (4.10) uses the general definition of fraction unreacted in a flow system. It is moles out divided by moles in. The corresponding, general definition of conversion is... 

The double integral in Equation (8.4) is a fairly general definition of the mixing-cup average. It is applicable to arbitrary velocity profiles and noncircular cross sections but does assume straight streamlines of equal length. Treatment of curved streamlines requires a precise and possibly artificial definition of the system boundaries. See Nauman and Buffham. ... 

Peedc-to-peak resolution in SEC can be calculated by the ratio of peak separation at the peak maxiaut to the sum of the baseline peak widths. This general definition of resolution is less useful in SEC, where a measure of the ability of the column to separate solutes of different molecular weight is required. For this purposes, we define a new term, the specific resolution factor, R, which relates peak resolution to sample molecular weight, assuming all measurements are made within the linear region of the molecular weight calibration curve, equation (4.41)... 

Note 7 There are definitions of linear viscoelasticity which use integral equations instead of the differential equation in Definition 5.2. (See, for example, [11].) Such definitions have certain advantages regarding their mathematical generality. However, the approach in the present document, in terms of differential equations, has the advantage that the definitions and descriptions of various viscoelastic properties can be made in terms of commonly used mechano-mathematical models (e.g. the Maxwell and Voigt-Kelvin models). 

In this section, we introduce generalized definitions of sets of reciprocal basis vectors, and of corresponding projection tensors, which include the dynamical reciprocal vectors and the dynamical projection tensor introduced in Section VI as special cases. These definitions play an essential role in the analysis of the constrained Langevin equation given in Section IX. 

A general definition of the heat capacity is given by the equation... 

The risk index defined in Equation 6.1 (see Section 6.2.1) is intended to provide a measure of the potential risk that arises from disposal of any waste that contains hazardous substances. In Section 6.3, the general definition of the risk index is elaborated and recommendations on suitable approaches to calculating the risk index for individual hazardous substances are presented. For purposes of developing a comprehensive and risk-based waste classification system, a simple method of calculating the risk from disposal of mixtures of hazardous substances is needed. The method must take into account that the allowable concentrations of particular hazardous substances in waste of a given class generally will be lower when multiple substances are present than when only a single substance is present. Such a method is presented and discussed in this Section. 

This equation is used as a general definition of the activation energy whether or not A is actually a constant. For the model above we get... 

A more general approach43) to the calculation of x which does not rely on the assumption of the Van Vleck equation uses the general definition (2)... 

Rudin and Strathdee (1974) remarked that the equations presented for the viscosity of dilute polymer solutions were valid approximately up to the critical concentration. This leads to a more general definition of a concentrated polymer solution, viz. a solution for which c > ccr. 

Third-order reaetions can be classified into three distinct types according to the general definition. If the stoichiometric equation is... 

In the operator L, the first term represents convection and the second diffusion. Equation (44) therefore describes a balance of convective, diffusive, and reactive effects. Such balances are very common in combustion and often are employed as points of departure in theories that do not begin with derivations of conservation equations. If the steady-flow approximation is relaxed, then an additional term, d(p(x)/dt, appears in L this term represents accumulation of thermal energy or chemical species. For species conservation, equations (48) and (49) may be derived with this generalized definition of L, in the absence of the assumptions of low-speed flow and of a Lewis... 

Although, for brevity, the subscript i was previously said to identify a particular species, it will be recalled from the general definition in Section A.l that i actually identifies a particular species in a particular phase. Hence equation (21) also expresses the condition for phase equilibrium. For example. 

On inserting these expressions into equation (35), we obtain the general definition of the moment of the electric dipole for an arbitrary microsystem ... 

Often referred to as the solvent cohesive energy density, the Hildebrand solubility parameter is considered to be a measure of the solvent contribution to the cavity term, and is used as a correction factor in the - solvatochromic equation. It is related to the general definition of London cohesive energy between two interacting species ... 

Another general theorem 9>1( states that the set of NO s associated with every eigenfunction of the Schrodinger equation has definite symmetry properties. In particular, for a planar molecule the natural orbitals are either a or n orbitals. Therefore, a and n orbitals have a physical meaning independent of any model assumption or approximation. By adding the occupation numbers of each species of orbitals, one defines... 

Equation (10.111) has the same form as Eq. (10.107), however, the definition (10.105) is replaced by a more general definition involving the time-dependent density operator of the bath. 

More generally, any force could be used to move the particles, so a more general definition of this type of transport coefficient will be the mobility diffusion coefficient, Du = ksTulci. Eq. (11.66)). Note that while this relationship between the conductivity and the diffusion coefficient was derived for noninteracting carriers, we now use this equation as a definition also in the presence of interparticle interactions, when o is given by Eq. (11.76). 

Equations (B.2) demonstrate that u and v violate condition (1) of Theorem I given in Eq. (3.5), and, thus, are not norm-preserving. However, since they relate the jn to the a)u), the effective Hamiltonian h which they produce should be identical to H. The general definition (2.10) indeed implies that h is given by... 

Lewis [13] proposed the electronic theory of acids and bases and gave a more general definition of acids and bases in its framework. Acids are determined as acceptors of an electron pair, and its donors are classified as bases. The principal scheme of the Lewis acid-base interaction is described by the following equation ... 

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